Existence of a minimal non-scattering solution to the mass-subcritical generalized Korteweg-de Vries equation

2016/02/17 by Masaki, Satoshi, Segata, Jun-ichi · 3 citations
#35B40 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 35Q53 #Secondary 35B30

paper · doi:10.48550/arxiv.1602.05331

Abstract

In this article, we prove existence of a non-scattering solution, which is minimal in some sense, to the mass-subcritical generalized Korteweg-de Vries (gKdV) equation in the scale critical ^Lr space. We construct this solution by a concentration compactness argument. Then, key ingredients are a linear profile decomposition result adopted to ^Lr-framework and approximation of solutions to the gKdV equation which involves rapid linear oscillation by means of solutions to the nonlinear Schr"odinger equation.

Cited by

• Characterization of Vanishing Campanato Spaces via Ball Banach Function Spaces and Its Applications
• The preduals of Banach space valued Bourgain-Morrey spaces
• Sharp Brezis--Seeger--Van Schaftingen--Yung Formulae for Higher-Order Gradients in Ball Banach Function Spaces

Related

• Refinement of Strichartz estimate for Airy equation in non-diagonal case and its application
• On the mass-critical generalized KdV equation
• Global well-posedness and scattering for the defocusing, mass - critical\n generalized KdV equation
• On minimal non-scattering solution for focusing mass-subcritical nonlinear Schrödinger equation
• A sharp scattering condition for focusing mass-subcritical nonlinear Schrödinger equation